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Quantum Spin
Spin is a fundamental property of quantum particles. It is conserved and quantised into units of Planck's constant. Light-matter interaction is the heart of quantum physics and the photoelectric effect was the experiment that introduced quantum concepts to modern physics. Background: The quantisation of light into particles called photons was the first step to understanding both the photoelectric effect and blackbody radiation. All bosons have integer spin, photons have spin 1, either left or right (+1 or -1) - where the units are in multiples of the reduced Planck's constant. ... A single coherent photon requires a single emitter and absorber in its timeline. Every photon is eventually absorbed somewhere, or it goes forever (time is menaingless). Similarly, in reverse time the photon has to have an emitter to create it. This is to say that every timeline must have a beginning and an end, but taking it to the quantum limit. This implies that for quantised light to exist there must exist quantised matter - single particles with quantised energy transitions to radiate from. Light and matter imply one another in the quantum sense. (Yin and Yang) In the more classical picture, this still holds but rather light implies a material realm in which to cause field fluctuations. Heree 'matter' comes to not mean physical mass-carrying particles, but rather implies a space-time in which light can be defined. This space-time will be referred to as 'matter' at times, but really refers more broadly to the entire realm of material existence. So, in this sense 'light-matter interaction' is actually all interactions we can possibly describe. One might argue that interactions such as ionic bonds are not light-matter interactions but this presumes that charge is a fundamental property of particles, rather than an emergent one. --- Zeeman: (and gyromag) A spin in an external field will experience a retardation or acceleration of its frequency dependent on whether it is aligned with or against this field. This manifests as an energy splitting between spin-down and spin-up - the Zeeman splitting. The amount of splitting is determined by the gyromagnetic ratio of the spin. --- Driving between states: Zeeman splitting introduces indegeneracy and causes a frequency difference between spin-up and spin-down, hence a phase difference between them, also. The absolute phase is arbitrary (depends on your reference frame) but the relative phase is determined once you fix a starting point in time. This is generally most usefully defined as the point at which the spin is first excited resonantly by a driving field. A driving field is an electromagnetic field oscillating at a frequency that is equal to the frequency difference of the Zeeman-split states. Hence, the energy of its photons is equal to the energy difference between the two eigenstates (the two allowable energy levels). Precession: The reason a driving field at this frequency causes transitions is because 1. the driving field is perpendicular to the external field, meaning that it introduces a new axis for spin and new eigenstates for the system, 2. non-eigenstates 'precess' (that is, periodically rotate) around the eigenstate axis, and 3. because the new axis is rotating at the same frequency as the precessional frequency (Larmor frequency) of the main axis, we can simply look at the new field from a point of view where nothing is rotating, because it 'tracks' the state as it precesses. The result of these 3 things is that a field rotating at the Larmor frequency in a plane perpendicular to the external field, basically causes the eigen-axis of the system to tilt by a small angle from it's z-axis and this new tilted axis then spins around the old axis at the same frequency as the state does. Hence, from the perspective of the state (in the rotating frame), the new axis is a static shift in the system's magnetic field. In this rotating frame, there is no B0 field (external field) since the rotating frame cancels it out. Hence, we are left only with the slight tilt component, which is now completely perpendicular to the original eigenstates. In this basis, the old eigen-states of spin-up and spin-down are not eigenstates and are in fact periodically swapped due to secondary precession around this x-like B1 component (the perpendicular quasi-static field). This secondary precession is generally at a much lower frequency than the B0 field, since the B1 field is small. --- Gyromagnetic ratio: (I still don't have an answer for what this fundamentally is, I would like to find this out before writing my thesis) The gyromagnetic ratio is the conversion factor that describes what frequency shift a particle will gain/lose when subjected to a magnetic field. For an electron it is -28 GHz/T (gigahertz per Tesla). Using the Toroidal Photon Model as a basis this would imply that spin-up and spin-down electrons are somehow different manifestations of the same photon when in 0 field (i.e. degenerate = same frequency) but when subjected to a non-zero field then the internal energy of the photon in each experiences a shift up or down in energy/frequency. Somehow, interaction of this toroidal photon with an external field causes the photon energy to take one of two possible stable values (eigen-energies, eigen-states). --- Nuclear Spin: Nuclear spin is ... (more complex than electron spin, due to a nucleus being composed of many separate spin particles - protons and neutrons - themselves being composed of quarks, whereas an electron is a fundamental particle). Toroidal Photon Models for hadrons (quark-containing particles) exist but are not as well studied as for the electron. Category:Quantum Category:Spin Category:Physics